In this experiment, you will investigate an electrical circuit. (a) Set up the circuit shown in Fig. 1.1. The distance $x$ between the crocodile clips should be approximately $40\text{ cm}$. (i) Measure and record $x$. $x$ = \_\_\_\_\_\_ (ii) Close the switch. (iii) Record the ammeter reading $I_1$. $I_1$ = \_\_\_\_\_\_ (iv) Open the switch. (i) Connect an additional lead L to the circuit as shown in Fig. 1.2. (ii) Close the switch. (iii) Record the ammeter reading $I_2$.…

(b)(i) x = 40.0 cm (example) · (b)(ii) Switch closed · (b)(iii) I1 = 0.35 A (example) · (b)(iv) Switch opened · (c)(i) Lead L connected as in Fig. 1.2 · (c)(ii) Switch closed · (c)(iii) I2 = 0.42 A (example) · (c)(iv) Switch opened · (c)(v) Lead L removed · (d) Table of six readings with x, I1, I2 and I2/I1 (example shown) · (e)(i) Graph of I2/I1 (y) against x (x-axis) plotted · (e)(ii) Straight line of best fit drawn · (e)(iii) gradient = 8.8×10^-3 cm^-1, y-intercept = 0.85…

Physics 9702/31 — May/June 2017

Cambridge AS Level · Advanced Practical Skills · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Manipulation, Measurement and Observation · Presentation of Data and Observations · Analysis, Conclusions and Evaluation

Q1Manipulation, Measurement and ObservationPresentation of Data and ObservationsAnalysis, Conclusions and EvaluationFree sample

In this experiment, you will investigate an electrical circuit.

(a) Set up the circuit shown in Fig. 1.1.

Fig. 1.1

The distance $x$ between the crocodile clips should be approximately $40\text{ cm}$ .

(b)

(i)

Measure and record $x$ .

$x$ = ______

DifficultyEasy

Worked solution

Answer

Measure $x$ with a metre rule.

Example (to nearest $1\ \text{mm}$ ):

x = 40.0\ \text{cm}

Final answer

x = 40.0 cm (example)

Detailed explanation

Background Concept

A length measurement should be taken with an instrument of suitable resolution (here, a metre rule). You must record the value to match the instrument’s smallest sensible division (typically $1\ \text{mm}$ on a standard metre rule), and you should read the scale without parallax error.

Understanding the Question

You are asked to measure the separation $x$ between the two crocodile clips on the wire, which should be about $40\ \text{cm}$ . The required response is a recorded value of $x$ .

Approach

Align the metre rule with the wire.
Read the positions of the two clip contact points on the wire.
Calculate $x$ as the difference between the two position readings.
Record $x$ to an appropriate precision.

Step-by-Step Reasoning

Identify the exact contact points where each crocodile clip touches the wire (not the outer edge of the clip).
Read the position of each contact point on the metre rule at eye level.
Compute the separation:

x = x_2 - x_1

Record the result to the nearest $1\ \text{mm}$ (or the smallest clear division available).

Key Takeaways

Measure between the correct points.
Use a difference of two readings to reduce zero/end errors.
Record with suitable precision.

Common Mistakes

Measuring from the ends of the crocodile clips rather than the contact points.
Parallax error from viewing the scale at an angle.
Writing too many decimal places (false precision) or too few (loss of precision).

Things to Be Careful About

Ensure the clips are firmly attached and not slipping along the wire.
Keep the metre rule parallel to the wire and note the unit used ( $\text{cm}$ or $\text{m}$ ) consistently for later graphing.

Techniques used

measure a length using a metre rulerecord a reading to an appropriate precisionavoid parallax when reading a scale

(ii)

Close the switch.

DifficultyEasy

Worked solution

Answer

Close the switch.

Final answer

Switch closed

Detailed explanation

Background Concept

Closing a switch completes the circuit so current can flow. In practical work, you often keep the switch open except when taking readings to reduce heating of components (which can change resistances).

Understanding the Question

This step instructs you to complete the circuit so that the ammeter can show a steady current for reading $I_1$ .

Approach

Close the switch only when you are ready to take the ammeter reading.

Step-by-Step Reasoning

With the circuit correctly connected, closing the switch completes the loop.
Current then flows through the ammeter, producing a reading.

Key Takeaways

Close the switch to take readings; open it between readings to reduce heating.

Common Mistakes

Leaving the switch closed for long periods, causing the wire/resistor to warm up and change current.

Things to Be Careful About

Ensure connections are secure before closing the switch.
If the ammeter reading is off-scale, open the switch immediately and change range.

Techniques used

operate a switch safelyfollow the stated procedure in sequence

(iii)

Record the ammeter reading $I_1$ .

$I_1$ = ______

DifficultyEasy

Worked solution

Answer

Record the current $I_1$ from the ammeter.

Example:

I_1 = 0.35\ \text{A}

Final answer

I1 = 0.35 A (example)

Detailed explanation

Background Concept

An ammeter measures current and must be connected in series. The reading should be taken on a suitable range to avoid overloading and to give good resolution. Record the value with an appropriate number of decimal places based on the meter’s resolution.

Understanding the Question

With the circuit in the Fig. 1.1 configuration and the switch closed, you must read and record the ammeter current as $I_1$ .

Approach

Choose a safe range first (highest range), then reduce if needed for better precision.
Wait briefly for the reading to settle.
Record $I_1$ with unit $\text{A}$ .

Step-by-Step Reasoning

If the ammeter is analogue, identify the correct scale and multiply by any range factor.
If it is digital, read directly from the display.
Record the reading, e.g.

I_1 = 0.35\ \text{A}

(Your value will depend on your circuit and $x$ .)

Key Takeaways

Correct connection (series) and correct range are essential.
Record current with unit and sensible precision.

Common Mistakes

Using the wrong range factor on an analogue meter.
Forgetting the unit.
Reading the scale from an angle (parallax) on analogue meters.

Things to Be Careful About

Heating of the wire changes resistance and therefore the current; take the reading promptly after closing the switch.
Ensure the ammeter reads zero (or note any zero error) before starting.

Techniques used

read an ammeter scale (or digital display) correctlyselect an appropriate ammeter rangerecord a value with correct precision and unit

(iv)

Open the switch.

DifficultyEasy

Worked solution

Answer

Open the switch.

Final answer

Switch opened

Detailed explanation

Background Concept

Opening the switch breaks the circuit so current stops flowing. This reduces heating of the wire/resistor, which helps keep conditions consistent for subsequent readings.

Understanding the Question

After recording $I_1$ , you are instructed to open the switch before making changes or taking the next set of readings.

Approach

Open the switch immediately after taking the reading.

Step-by-Step Reasoning

With the switch opened, the current becomes zero.
This prevents further temperature rise in the wire and helps improve repeatability.

Key Takeaways

Open the switch between readings to minimise systematic changes.

Common Mistakes

Leaving the circuit energised while adjusting crocodile clips.

Things to Be Careful About

If using a power supply, avoid short circuits when repositioning clips; keeping the switch open reduces risk.

Techniques used

follow the stated procedure in sequencereduce heating effects by opening the switch between readings

(c)

(i)

Connect an additional lead L to the circuit as shown in Fig. 1.2.

Fig. 1.2

DifficultyMedium-Easy

Worked solution

Answer

Connect the additional lead $L$ exactly as in Fig. 1.2 (between the stated junctions).

Final answer

Lead L connected as in Fig. 1.2

Detailed explanation

Background Concept

In circuit practicals, altering the circuit configuration changes the total resistance and therefore the current. Correctly connecting leads to the intended junctions is crucial; a wrong connection can create an unintended short circuit or open circuit.

Understanding the Question

You must add an extra lead $L$ to change the circuit from the Fig. 1.1 arrangement to the Fig. 1.2 arrangement. The key skill is correctly following the diagram and connecting to the correct nodes.

Approach

Locate the two junctions indicated in Fig. 1.2.
Connect one end of lead $L$ to the first junction and the other end to the second junction.
Ensure all other components remain as in Fig. 1.1.

Step-by-Step Reasoning

Identify junctions (nodes) rather than components: junctions are where wires/components meet.
With the switch open, attach lead $L$ firmly so that it makes good electrical contact.
Check visually that the circuit now matches Fig. 1.2 before closing the switch.

Key Takeaways

Always connect based on junctions in the circuit diagram.
Keep the switch open while rewiring.

Common Mistakes

Attaching lead $L$ to the wrong side of a component (wrong node).
Creating a short circuit by connecting across the power supply or bypassing the ammeter.

Things to Be Careful About

Ensure crocodile clips are not touching each other or other conductive parts.
Poor contacts introduce extra resistance and can affect $I_2$ .

Techniques used

modify a circuit according to a given diagrammake secure electrical connections at specified junctionscheck that the circuit matches the required configuration

(ii)

Close the switch.

DifficultyEasy

Worked solution

Answer

Close the switch.

Final answer

Switch closed

Detailed explanation

Background Concept

Closing the switch completes the (modified) circuit so that current flows and the ammeter can display $I_2$ .

Understanding the Question

With lead $L$ connected (Fig. 1.2), you must now energise the circuit to measure $I_2$ .

Approach

Close the switch only when ready to read the ammeter.

Step-by-Step Reasoning

Close switch to allow current to flow.
Wait for a steady reading.

Key Takeaways

Consistent procedure improves reliability.

Common Mistakes

Leaving the switch closed too long, causing heating.

Things to Be Careful About

If the reading is much larger than before, open the switch and increase the ammeter range.

Techniques used

operate a switch safelyfollow the stated procedure in sequence

(iii)

Record the ammeter reading $I_2$ .

$I_2$ = ______

DifficultyEasy

Worked solution

Answer

Record the current $I_2$ from the ammeter.

Example:

I_2 = 0.42\ \text{A}

Final answer

I2 = 0.42 A (example)

Detailed explanation

Background Concept

The ammeter measures the total current in the series part of the circuit. Changing the circuit (by adding $L$ ) changes the current, so $I_2$ is generally different from $I_1$ .

Understanding the Question

With the switch closed and lead $L$ connected, you must read and record the new ammeter current as $I_2$ .

Approach

As for $I_1$ : choose a suitable range, wait for a stable reading, and record with unit.

Step-by-Step Reasoning

Confirm the ammeter is still in series and not bypassed.
Read the current and record it, e.g.

I_2 = 0.42\ \text{A}

(Your value will depend on your circuit and $x$ .)

Key Takeaways

Record measurements consistently and clearly.

Common Mistakes

Reading the wrong scale or range.
Omitting the unit.

Things to Be Careful About

Take the reading promptly to reduce the effect of temperature rise in the wire.

Techniques used

read an ammeter scale (or digital display) correctlyselect an appropriate ammeter rangerecord a value with correct precision and unit

(iv)

Open the switch.

DifficultyEasy

Worked solution

Answer

Open the switch.

Final answer

Switch opened

Detailed explanation

Background Concept

Opening the switch stops the current, helping to keep the wire temperature (and therefore resistance) as constant as possible between readings.

Understanding the Question

After measuring $I_2$ , you must open the switch before disconnecting $L$ .

Approach

Open the switch immediately after reading the ammeter.

Step-by-Step Reasoning

Break the circuit by opening the switch.
Then it is safe to alter the circuit connections.

Key Takeaways

Open switch before rewiring.

Common Mistakes

Removing $L$ while the switch is closed.

Things to Be Careful About

Avoid accidental short circuits when leads are moved.

Techniques used

follow the stated procedure in sequencereduce heating effects by opening the switch between readings

(v)

Remove L. The circuit is now as shown in Fig. 1.1.

DifficultyEasy

Worked solution

Answer

Remove lead $L$ so the circuit returns to Fig. 1.1.

Final answer

Lead L removed

Detailed explanation

Background Concept

To obtain paired readings $(I_1, I_2)$ for the same $x$ , you must switch between the two circuit configurations in a controlled way. Returning to the original configuration ensures the next $I_1$ reading is taken under the same circuit conditions as before.

Understanding the Question

You are instructed to remove $L$ so the circuit is again as in Fig. 1.1, ready for the next reading of $I_1$ at a new value of $x$ .

Approach

With the switch open, disconnect lead $L$ and check the remaining circuit matches Fig. 1.1.

Step-by-Step Reasoning

Ensure no current flows (switch open).
Disconnect lead $L$ from both junctions.
Inspect the circuit: only the original connections in Fig. 1.1 remain.

Key Takeaways

Resetting correctly prevents mixing configurations.

Common Mistakes

Forgetting to remove $L$ , leading to incorrect $I_1$ values for later readings.

Things to Be Careful About

Keep connections consistent; do not move crocodile clips unless you are changing $x$ deliberately.

Techniques used

restore the circuit to its original configurationcheck the circuit matches the required diagram before proceeding

(d)

Increase $x$ and repeat (b) and (c) until you have six sets of readings of $x$ , $I_1$ and $I_2$ .

Record your values in a table. Include values of $\frac{I_2}{I_1}$ in your table.

10M

DifficultyMedium

Worked solution

Answer

Obtain six sets of readings for $x$ , $I_1$ and $I_2$ over an increased range of $x$ , and calculate $I_2/I_1$ for each set.

Example of a suitable table:

$x / \text{cm}$	$I_1 / \text{A}$	$I_2 / \text{A}$	$I_2/I_1$
$40.0$	$0.35$	$0.42$	$1.20$
$45.0$	$0.33$	$0.41$	$1.24$
$50.0$	$0.31$	$0.40$	$1.29$
$55.0$	$0.29$	$0.39$	$1.34$
$60.0$	$0.27$	$0.38$	$1.41$
$65.0$	$0.26$	$0.37$	$1.42$

Final answer

Table of six readings with x, I1, I2 and I2/I1 (example shown)

Detailed explanation

Background Concept

Good experimental data must be (i) sufficiently numerous, (ii) spread over a suitable range of the independent variable, and (iii) clearly presented. A results table should include raw measurements (here $x$ , $I_1$ , $I_2$ ) and any calculated quantities required by the question (here the ratio $I_2/I_1$ ).

Table conventions in Cambridge practical papers:

One table containing all results.
Clear column headings with quantity and unit, e.g. $x/\text{cm}$ , $I_1/\text{A}$ .
Consistent decimal places/significant figures within each column.

Understanding the Question

You must increase the clip separation $x$ and, for each new $x$ , repeat the procedures in (b) and (c) to obtain paired currents $I_1$ (Fig. 1.1) and $I_2$ (Fig. 1.2). You need six sets of $(x, I_1, I_2)$ and must also calculate and record $I_2/I_1$ .

Approach

Choose at least six values of $x$ that are reasonably spaced (e.g. every $5\ \text{cm}$ ) and cover a good range.
For each $x$ $x$ :
- measure and record $x$ ,
- measure $I_1$ with the original circuit,
- add lead $L$ and measure $I_2$ ,
- open the switch between readings.
Compute $I_2/I_1$ for each row and record it to a sensible number of significant figures.

Step-by-Step Reasoning

Pick a sequence such as $x = 40\ \text{cm}$ to $65\ \text{cm}$ .
For each $x$ , take $I_1$ and $I_2$ promptly after closing the switch to reduce heating effects.
Calculate the ratio for each row:

\frac{I_2}{I_1} = \frac{\text{(ammeter reading with }L\text{ connected)}}{\text{(ammeter reading without }L\text{)}}

Example for the first row:

\frac{I_2}{I_1} = \frac{0.42}{0.35} = 1.20

Keep the ratio to (typically) 2 or 3 significant figures, consistent across the ratio column.

Key Takeaways

Collect enough data points (six) across a range of $x$ .
Present data clearly in one table with headings and units.
Calculate and include required derived quantities.

Common Mistakes

Fewer than six sets of readings.
Missing units in headings (e.g. writing just $x$ rather than $x/\text{cm}$ ).
Inconsistent decimal places within a column.
Arithmetic errors when calculating $I_2/I_1$ .

Things to Be Careful About

Use the same unit for $x$ throughout (if you use $\text{cm}$ in the table, use $\text{cm}$ on the graph).
Avoid heating: open the switch between readings and do not leave current flowing.
Ensure $x$ is the clip separation, not the position of a single clip.

Techniques used

repeat measurements over a suitable range of the independent variabletabulate raw and derived quantities with correct headings and unitscalculate a ratio for each set of readingsuse consistent significant figures within each column

(e)

(i)

Plot a graph of $\frac{I_2}{I_1}$ on the $y$ -axis against $x$ on the $x$ -axis.

DifficultyMedium-Easy

Worked solution

Answer

Plot $\left(\frac{I_2}{I_1}\right)$ on the $y$ -axis against $x$ on the $x$ -axis, with axes labelled (including units for $x$ ) and points plotted accurately using a suitable scale.

Final answer

Graph of I2/I1 (y) against x (x-axis) plotted

Detailed explanation

Background Concept

A graph is used to test a relationship and to obtain constants from the gradient and intercept. Good graph technique earns marks for:

correct choice of axes,
clear labels with units,
sensible scales (use at least half of the grid in both directions),
accurate plotting.

Understanding the Question

You must plot a graph with $y = I_2/I_1$ and $x$ on the horizontal axis. The data come from your table in (d).

Approach

Horizontal axis: $x$ (use the same unit as your table, commonly $\text{cm}$ ).
Vertical axis: $I_2/I_1$ (dimensionless).
Choose scales so the plotted points occupy a large area of the grid.
Plot all six points clearly.

Step-by-Step Reasoning

Draw axes and label:
- $x/\text{cm}$ (or $x/\text{m}$ ),
- $I_2/I_1$ .
Choose a scale such as $2\ \text{cm}$ per $5\ \text{cm}$ on the $x$ -axis (example) and a scale on the $y$ -axis that spreads the points.
Plot each point $(x, I_2/I_1)$ using small crosses.

Key Takeaways

Correct labelling and sensible scaling are essential.

Common Mistakes

Swapping axes (plotting $x$ on $y$ -axis).
Missing units for $x$ .
Using awkward scales (e.g. 3 squares = 7 units) that reduce accuracy.

Things to Be Careful About

$I_2/I_1$ has no unit; do not invent one.
Plot points carefully; large blobs instead of fine crosses reduce accuracy when drawing a best-fit line.

Techniques used

choose appropriate axes and scaleslabel axes with quantity and unitplot experimental points accurately

(ii)

Draw the straight line of best fit.

DifficultyMedium-Easy

Worked solution

Answer

Draw a single straight line of best fit through the plotted points (balanced with roughly equal scatter above and below).

Final answer

Straight line of best fit drawn

Detailed explanation

Background Concept

A best-fit line represents the overall trend of data when random uncertainties cause scatter. For a linear relationship, you should draw a straight line that is ‘balanced’—not forced through every point.

Understanding the Question

After plotting $I_2/I_1$ against $x$ , you must draw the straight line that best represents the trend.

Approach

Use a ruler.
Aim for approximately equal numbers of points above and below the line.
Do not join point-to-point.

Step-by-Step Reasoning

Place the ruler so the line passes through the central region of the plotted points.
Check that the line is not overly influenced by one outlier.
Draw a thin, clear straight line.

Key Takeaways

Best-fit means representing the trend, not connecting dots.

Common Mistakes

Forcing the line through the origin when not justified.
Drawing a zig-zag line between points.

Things to Be Careful About

If one point is clearly anomalous, the best-fit line should follow the other points; do not automatically force the line to pass through the anomaly.

Techniques used

draw a balanced straight line of best fitavoid joining point-to-pointignore anomalous points appropriately

(iii)

Determine the gradient and $y$ -intercept of this line.

gradient = ______

$y$ -intercept = ______

DifficultyMedium

Worked solution

Working

Using two well-separated points on the best-fit line (example): $(40.0\ \text{cm},\ 1.20)$ and $(65.0\ \text{cm},\ 1.42)$ ,

\text{gradient} = \frac{\Delta y}{\Delta x} = \frac{1.42 - 1.20}{65.0 - 40.0} = 8.8 \times 10^{-3}\ \text{cm}^{-1}

$y$ -intercept (from line / using $c = y - mx$ ):

\text{intercept} = 1.20 - (8.8 \times 10^{-3})(40.0) \approx 0.85

Answer

\text{gradient} = 8.8 \times 10^{-3}\ \text{cm}^{-1}

y\text{-intercept} = 0.85

Final answer

gradient = 8.8×10^-3 cm^-1, y-intercept = 0.85 (example)

Detailed explanation

Background Concept

For a straight-line graph, the gradient (slope) is

\text{gradient} = \frac{\Delta y}{\Delta x}

and the $y$ -intercept is the value of $y$ when $x = 0$ . In practical graphs, you should use points on the best-fit line (not necessarily your original data points) and choose them far apart to reduce percentage uncertainty.

Units:

Here $y = I_2/I_1$ is dimensionless.
Therefore the gradient has units of $1/x$ (e.g. $\text{cm}^{-1}$ if $x$ is in cm).

Understanding the Question

You must find the gradient and $y$ -intercept of your best-fit straight line on the graph of $I_2/I_1$ (vertical axis) against $x$ (horizontal axis).

Approach

Select two points on the drawn best-fit line that are widely separated.
Read their coordinates accurately.
Compute gradient using $\Delta y/\Delta x$ .
Find intercept either by reading where the line crosses the $y$ -axis or by substituting into $y = mx + c$ .

Step-by-Step Reasoning

Choose two points far apart (example values shown in the solution).
Calculate:

\text{gradient} = \frac{1.42 - 1.20}{65.0 - 40.0}

Because $x$ is in cm in this example, the gradient unit is $\text{cm}^{-1}$ .
To obtain the intercept, rearrange $y = mx + c$ :

c = y - mx

and substitute one of the points.

Alternatively, extend the line to $x = 0$ and read the intercept directly (but calculating from $c = y - mx$ is often more precise if reading $x=0$ is off the grid).

Key Takeaways

Use the best-fit line, not a pair of raw points close together.
Use a large triangle / widely spaced points to reduce uncertainty.
Gradient units come from $y$ units divided by $x$ units.

Common Mistakes

Using $\Delta x/\Delta y$ instead of $\Delta y/\Delta x$ .
Using two neighbouring points, giving a large uncertainty in the gradient.
Forgetting the gradient unit.

Things to Be Careful About

Read coordinates carefully from the axes (especially if scales are not 1 per square).
Keep consistent units: if you plotted $x$ in $\text{cm}$ , your gradient must be in $\text{cm}^{-1}$ (unless you convert).

Techniques used

determine gradient using a large triangle on the best-fit lineread y-intercept from the best-fit linecalculate $\Delta y/\Delta x$ with consistent units

(f)

It is suggested that the quantities $I_1$ , $I_2$ and $x$ are related by the equation

\frac{I_2}{I_1} = Px + Q

where $P$ and $Q$ are constants.

Using your answers in (e)(iii), determine values for $P$ and $Q$ .
Give appropriate units.

$P$ = ______

$Q$ = ______

DifficultyMedium-Easy

Worked solution

Working

Given

\frac{I_2}{I_1} = Px + Q

Comparing with $y = mx + c$ :

P = \text{gradient},\qquad Q = y\text{-intercept}

Using (e)(iii) (example):

P = 8.8 \times 10^{-3}\ \text{cm}^{-1}

Q = 0.85

Answer

P = 8.8 \times 10^{-3}\ \text{cm}^{-1}

Q = 0.85\ \text{(no unit)}

Final answer

P = gradient (cm^-1), Q = y-intercept (no unit) (example values shown)

Detailed explanation

Background Concept

A linear relationship has the form

y = mx + c

where $m$ is the gradient and $c$ is the $y$ -intercept. If you plot $y$ against $x$ and obtain a straight line, you can identify constants in the equation by matching symbols to this standard form.

Units:

$I_2/I_1$ is a ratio of two currents, so it is dimensionless.
Therefore $Q$ is dimensionless.
Since $Px$ must also be dimensionless, $P$ must have units of $1/x$ .

Understanding the Question

You are given

\frac{I_2}{I_1} = Px + Q

and asked to determine $P$ and $Q$ using your gradient and intercept from (e)(iii), including appropriate units.

Approach

Recognise that the graph in (e) was $y = I_2/I_1$ versus $x$ .
Compare directly with $y = mx + c$ .
Set $P = m$ and $Q = c$ .
Assign units based on what you used for $x$ .

Step-by-Step Reasoning

From the plotted variables:

y = \frac{I_2}{I_1},\quad x = x

The equation matches $y = Px + Q$ , so:

P = \text{gradient},\qquad Q = y\text{-intercept}

If $x$ was plotted in $\text{cm}$ , then

[P] = \text{cm}^{-1}

and if $x$ was plotted in $\text{m}$ , then $[P] = \text{m}^{-1}$ .

$Q$ has no unit because it is the value of the dimensionless ratio at $x=0$ .

Key Takeaways

Constants in a straight-line model are read from gradient and intercept.
Units come from the axes: dimensionless $y$ implies gradient has units of $1/x$ .

Common Mistakes

Giving $Q$ a unit (it should be dimensionless here).
Giving the wrong unit for $P$ by forgetting whether $x$ was in $\text{cm}$ or $\text{m}$ .

Things to Be Careful About

Use your own measured gradient and intercept values from (e)(iii), not values from raw data points.
State units explicitly for $P$ and state “no unit” (or omit units) for $Q$ .

Techniques used

match an experimental straight-line graph to $y = mx + c$identify constants from gradient and interceptdeduce units from the plotted quantities

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Q2Manipulation, Measurement and Observation · Analysis, Conclusions and Evaluation · Presentation of Data and Observations20M

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